hintsandthings.co.uk »Office

Mathematical shortcuts and tricks, methods of checking arithmetic


OFFICE

HOME
Garage –  Workshop
–  Office –  Library
–  Bathroom –  Living – 
Nursery
  Spare



Utility –  Kitchen –  Games
–  MusicGarden
–  Kennel

SEARCH
SITE

 



MATHEMATICAL SHORTCUTS

Handy shortcuts for checking calculations, without the need of a
calculator!

To check addition is correct –

  • add up the single digits of each individual number in the sum, until
    you are left with a single digit. 
  • add these single digits together until you are, once again, left with
    a single digit.
  • do the same with the total
  • these figures should be the same
EXAMPLE:
                                 
7745 + 3289  = 11034
                                                      
7+7+4+5       =  23
           2+3 = 5
                                                      
3+2+8+9       =  22
           2+2 = 4
                                                                                                         
  9
                                                      
1+1+0+3+4   =   

9

To check subtraction is correct:-

  • add together the total and the number you subtracted and this should
    equal the number you started with.
EXAMPLE:
                                  
4320 – 1978 = 2342
                                                      
1978+2342   =
4320

To check multiplication is
correct:-

  • divide the answer by one of the numbers being
    multiplied.
EXAMPLE:
                                
  27  x 19 =  513
                                                     
513 ÷ 19 =    27

To check division is
correct:-

  • multiply the answer by the number you originally
    divided by and this answer should be the same as the original number being divided.
EXAMPLE:
                                
798 ÷ 14   =    57
                                                   
    57 x 14   =

798

 

HANDY HINTS

If two columns of figures should balance but don’t, subtract one
total from the other and if the difference is 1, 10, 100, 9 or 99 you have probably made
an error in addition.


If the difference is divisible by 9 you have probably transposed a
figure (e.g.  written 89 instead of 98).

This was also sent in by KB who gave the following
illustration –

If your balance says 45.25 but your
statement says 42.55 – the difference is 2.70 which is
divisible by 9 so, therefore, it is probably a transposed figure.  You can see the 5
and 2 have been transposed.


To “square” a number (i.e. multiply a number by
itself e.g. 17 x 17)

Example A – 17 x 17

 

First partition the number  –  10, 7
Square the 10   (i.e. 10 x 10)
 
=
  100
Square the 7     (i.e.    7 x
  7)
  
 
=     49
Then 2 x (10 x 7)
   
 =
  140


17 x 17 

  =
   289

                


Example B – 52 x 52

Partition the number
          –  50, 2
Square the 50  (50 x 50)
  
 =
2,500 

(5 x 5 plus two noughts)

Square the 2    ( 2 x 2)
          
  =
       4
Then 2 x (50 x 2)   =
   200

52 x 52
   


 
  = 2,704

This shortcut was sent in by
Sue Knight – thanks.


An easy way to remember your nine times table is –

a:  The figures in the answer always total 9
            

e.g.       
2 x 9 = 18 (1+8 =
9):
              7 x 9 = 63 (6+3 = 9)

b:  Deduct 1 from the number you are multiplying and the second
number in the answer then becomes obvious (as it must
total 9).
               

To multiply 8 x 9
 

Deduct 1 from the 8 = 7 (this is the first number of the
answer)

The numbers in the answer always total 9 so the second number
must be 2     

Therefore 8 x 9 =72


Now for the 11 times table –

a:  Add together the digits you are multiplying  e.g. 33 x 11 add the 3 + 3 =6

b:  Place the the answer in between the two digits  e.g.
  363

Therefore 33 x 11 = 363

If the two digits add up to more than
ten (e.g. 48 x 11 where 4+8=
12) then you have to
add the 1 to the 4 and place the 2 in the middle of the two numbers. 

Therefore 48 x 11 = 528


If you ever need to find out the sum of all the numbers
between two given digits, here is the formula :-

ADD TOGETHER THE FIRST NUMBER AND THE LAST NUMBER IN THE SEQUENCE
THEN MULTIPLY BY THE NUMBER OF THE MIDDLE NUMBER IN THE SEQUENCE.

I will try to explain – say you wanted to find out the total of
numbers 7 through to 35.

i.e. 7+8+9 +10+11 an so on until..33+34+35.

First add the first number in the
sequence to the last number in the sequence, which in this case is –  7 + 35 = 42

Then to find the NUMBER of the middle digit in the sequence you
deduct the lowest number from the highest number, add 1 then divide by 2

i.e.  35 – 7 = 28 + 1 = 29
divided by 2 =
14.5

NOW MULTIPLY 42 X 14.5 = 609

SO THE SUM OF ALL FIGURES BETWEEN 7
AND 35 = 609


Now all you accountants out there – give us some more (or have you
forgotten them!) – contact us on june@hintsandthings.co.uk.

For more mathematical shortcuts
click here.
 


Google